Inter general manager Ernesto Paolillo hailed Leonardo as “the Coach of the future” after the historic achievement in Munich.
The Nerazzurri became only the second team in Champions League history to fight back from a first leg home defeat to qualify.
“It was a crucial victory wanted by the team, so we are all satisfied and proud,” Paolillo told Radio Sportiva after the 3-2 win over Bayern.
“I believed right to the end. Bayern's goals only came about because of our own defensive errors. In the second half Inter were clearly the better side and showed great determination to make up for the first leg.
“Leonardo will be the Coach of the future. He came to us for a long-term project and we want to introduce more young players. Aside from being a great tactician, Leonardo knows how to use psychology in football to help players overcome difficult moments and maintain team spirit.”
The master of that technique had been Jose Mourinho, taking Inter to the Treble last season.
“Mourinho sent us a message at the end of the game last night. He also sent one before the match, saying he was certain Inter would win. If we have a winning mentality, then it is also down to him.
“We were all so moved at the final whistle, as it was wonderful to see so many fans make the trip to Munich and even more waiting for us at the airport in Milan at 3am.
“We know it's difficult to target the Treble again, but we'll keep going for it as long as we can.”
Think you know your Italian football? Share your knowledge, tips and comments to win cash prizes in OLBG's tipster competition  - £5,000 monthly.